Experimental analysis of approaches to multidimensional conditional density estimation

Abstract

Recently several original methods for conditional density estimation (CDE) have been developed. The abundance of information comprised by the full conditional density of target variables is great when compared to the regression or quantile regression estimates. Still, there are only few independent experimental investigations of these methods, especially concerning a multidimensional target variable, and this paper aims to address this issue. We consider several approaches such as kernel density estimation, reduction to binary classification, Naïve Bayes, Bayesian Network, “varying coefficient” approach, random forests and Approximate Bayesian Computation applied to a conditional density estimation problem. We examine these methods when applying to various datasets together with the dependency of the methods’ performance on different parameters including the number of irrelevant covariates, smoothness, and flatness of the distribution. Considered datasets include artificial models with required properties and with the known exact value of CDE evaluation measure and a real-world dataset arisen from the problem of structure recognition by XANES spectra, which is reduced to a regression task with a complex multimodal probability distribution of the target variable. The special attention is paid to the computation of the evaluation measure as the methods based on the direct optimization of the loss employ its imprecise but fast approximation which results in the poor prediction quality for datasets with a small target variance.